{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T00:01:13Z","timestamp":1790640073333,"version":"4.1.0"},"reference-count":38,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,3,17]],"date-time":"2021-03-17T00:00:00Z","timestamp":1615939200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this paper, we present a decentralized unmanned aerial vehicle (UAV) swarm formation control approach based on a decision theoretic approach. Specifically, we pose the UAV swarm motion control problem as a decentralized Markov decision process (Dec-MDP). Here, the goal is to drive the UAV swarm from an initial geographical region to another geographical region where the swarm must form a three-dimensional shape (e.g., surface of a sphere). As most decision-theoretic formulations suffer from the curse of dimensionality, we adapt an existing fast approximate dynamic programming method called nominal belief-state optimization (NBO) to approximately solve the formation control problem. We perform numerical studies in MATLAB to validate the performance of the above control algorithms.<\/jats:p>","DOI":"10.3390\/a14030091","type":"journal-article","created":{"date-parts":[[2021,3,17]],"date-time":"2021-03-17T11:48:22Z","timestamp":1615981702000},"page":"91","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":31,"title":["UAV Formation Shape Control via Decentralized Markov Decision Processes"],"prefix":"10.3390","volume":"14","author":[{"given":"Md Ali","family":"Azam","sequence":"first","affiliation":[{"name":"Electrical Engineering, South Dakota School of Mines and Technology, Rapid City, SD 57701, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1961-657X","authenticated-orcid":false,"given":"Hans D.","family":"Mittelmann","sequence":"additional","affiliation":[{"name":"School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5511-4334","authenticated-orcid":false,"given":"Shankarachary","family":"Ragi","sequence":"additional","affiliation":[{"name":"Electrical Engineering, South Dakota School of Mines and Technology, Rapid City, SD 57701, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Waharte, S., Trigoni, N., and Julier, S. 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